Vibration isolation control for flexible structures restricts the response resulting from external disturbances to areas not requiring high precision positioning and/or pointing. This paper introduces adaptive feedback isolation controllers, based on Lyapunov theory, that regulate and allow tracking of the undisturbed (controlled) coordinates in a flexible structure. Under assumptions of inertially decoupled controlled and uncontrolled coordinates, symmetric and positive definite mass matrix for the controlled subsystem, asymptotically stable eigenvalues for the uncontrolled subsystem, and bounded disturbances, an adaptive regulator asymptotically drives the controlled coordinates to zero. Under similar assumptions, an adaptive tracking algorithm drives the controlled coordinates to desired time trajectories. Experimental results on a three mass system compare the response of the adaptive isolation controllers with standard PID control. The adaptive regulator provides faster transient decay than PID control using the same control effort. The adaptive tracking controller has the same tracking error of PID using 30% less control effort.

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